Question

	5. Suppose the coffee industry claimed that the average adult drinks 1.7 cups of coffee per day.
	To  test this claim, a random sample of 10 Coffee drinkers were selected
	and their average coffee consumption was found to be 2.0 cups per day.
	Assume the standard deviation of daily coffee consumption per day is 0.5 cups.
	Using α = 0.20 test the Hypothesis Is the Coffee consumption differs from the average coffee consumption?
	a.  State the Null Hypothesis and alternate Hypothesis.
	b.  use the Z statistical model test the Hypothesis at 0.10 significance level and the p value.
	c. Is the coffee industry's claim supported by this sample?

Answer 1

Population mean = U

Sample mean = x = 2 cups per day

Standard Deviation = s = 0.5 cups per day

Sample size = n = 10

Standard error of mean = se = s/n^0.5 = 0.5/10^0.5 = 0.16 cups per day

a) Hypotheses,

H0 : U = 1.7, against

H1 : U not = 1.7 (Two tailed test)

b) Zscore = (x - U)/se = (2 - 1.7)/0.16 = 1.875

p-value = 0.0304

As it is a two tailed test, so, comparing p-value with level of significance(a)/2 we get,

0.0304< 0.05

Thus, we reject the null hypothesis.

c) Hence, coffee industry’s claim that an adult consumes 1.7 cups of coffee per day on average is not supported by this sample.

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